1. Field of the Invention
The present invention is directed to a method and apparatus for improving the signal to noise ratio of an information carrying signal.
2. Description of Related Art
In the practice of many technologies, an information carrying signal is produced. A few examples of such technologies are imaging with a camera or opto-electronic sensor, radio and television communications, and medical imaging with magnetic resonance. The usefulness of the information carrying signal is dependent on its clarity, and noise in the signal, which is an inevitable result of physical and electrical processes, places a limitation on such clarity. Thus, it is desirable to be able to eliminate noise to the greatest degree possible, or, equivalently, to increase the signal to noise ratio of the information carrying signal.
Different approaches, such as those using various types of filters are known to improve signal to noise ratio. One type of approach, to which the present invention pertains, uses a mathematical operator known as a wavelet transform. Thus, it is well known that an electrical signal typically has an amplitude which varies with time, thus creating a frequency content in the signal. Certain types of information, for example, optical information, also has a spatial variance, and such is frequently converted to a time context in the electrical signal which results from the detection of the optical information.
To obviate noise, the electrical signal may be processed in the frequency domain, for instance, with a simple filter, or in a higher mathematical order domain known as a transform domain. For example, in the art of signal processing, the Fourier transform is a commonly used transform domain. However the wavelet transform domain possesses advantages over the Fourier domain because while the Fourier domain addresses only the frequency content of a signal, the wavelet transform places the frequency content within a spatial context. Thus, the wavelet transform is capable of producing improved signal to noise ratio as compared with the Fourier transform, including signals with sharper edges.
There are several approaches which are already known for using the wavelet transform for improving signal to noise ratio. However, each of these approaches includes disadvantages which are overcome by the present invention. The known approaches are as follows:
(a) The wavelet shrinkage approach described in Ideal Spatial Adaption via Wavelet Shrinkage, Donoho, D. L., and Johnstone, I. M., Technical Report/Revised Technical Report, Stanford University 1992, 1993 and 1994, Biometrika, 81:425-455. This approach uses wavelet decomposition to identify the different frequency/spatial components of the image or signal of interest. A statistically derived xe2x80x9cuniversal thresholdxe2x80x9d based upon the original image amplitude standard deviation (or estimate thereof) is then used to threshold or shrink the amplitudes of the wavelet coefficients. After an inverse wavelet transform is performed, the image or signal is recovered, but with somewhat reduced high frequency noise.
(b) The soft thresholding approach was developed as an improvement on wavelet shrinkage and uses an amplitude adaptive threshold to optimize the performance of the algorithm at each level of wavelet decomposition. See De-Noising via Soft Thresholding, Donoho, D. L., Technical Report 409, 1992 Department of Statistics, Stanford University.
(c) The cycle-spinning technique described in Translation-Invariant De-Noising, Coifman, R. R., and Donoho, D. L., Technical Report, Department of Statistics, Stanford University 1995, uses both the wavelet shrinkage approach [a] and soft thresholding approach [b], and applies the techniques to multiple phase-shifts of the input signal or image. The results for each phase shift are then averaged together, resulting in a reduction in noise compared to the input signal/image.
(d) The cross validation approach uses the soft thresholding technique mentioned previously in [b] and uses a curve fitting approach to the input data to develop a better noise estimate, and hence, a better threshold value, than the xe2x80x9cuniversal thresholdxe2x80x9d devised by Donoho et al. See Generalized Cross Validation for Wavelet Thresholding, Jansen, M., Malfait, M., Bultheel, A., 1996.
(e) The wavelet domain filtering approach is described in Wavelet Domain Filtering for Photon Imaging Systems Nowak, R. D., and Baraniuk, R. G., submitted April 1997 to IEEE Transactions on Image Processing. In this technique, the image acquisition period is subdivided into many shorter images, to form a series of images that are affected by the same Poisson noise process. A Wiener-type filter is constructed, using the input data to perform a cross-validation similar to the device in [d]. This technique is claimed to provide good noise removal properties, with a minimum of image degradation or edge softening.
A problem with all of the above techniques (a) to (e) is that they suffer from the need to develop an estimate of the noise in the image in order to compute an appropriate threshold. Because the noise may be composed of both Gaussian and Poisson components, as well as both additive and multiplicative errors, this limits the effectiveness of each of these approaches. For techniques [a] through [c], in fact, it appears that signal-to-noise improvement of greater than 1.2xc3x97 is unlikely. Technique [d], because of the cross-validation optimization process, has demonstrated a signal-to-noise improvement of approximately 1.5xc3x97 while technique [e] has somewhat better performance, with a demonstrated improvement of approximately 2.4xc3x97 in signal-to-noise. However, techniques [d] and [e], also require a large number of calculations to compute their optimized thresholds, and may not work well on complex images, due to the large numbers of feature edges present that could skew the noise estimates of these algorithms.
In distinction to the prior art, which as described above, uses amplitude thresholding of the noise components, the present invention uses frequency thresholding. The wavelet transform may be advantageously adapted to this approach since it has the capability of automatically classifying information according to frequencies.
Thus, in accordance with an aspect of the present invention, a method of improving the signal to noise ratio of an information carrying signal is provided comprising the steps of,
computing a wavelet transform of the information carrying signal up to a predetermined level,
from the wavelet transform, deriving a frequency thresholded signal which is indicative of noise, and
subtracting the frequency thresholded signal from the information carrying signal to provide a resultant signal having an improved signal to noise ratio.
With the use of the present invention, greater improvement in signal to noise ratio than with the prior art is obtainable. Also, since no thresholds need be computed and large numbers of calculations are avoided, much of the processing which is required by the prior art is eliminated.